Problem: $J$ is the midpoint of $\overline{CT}$ C J T If: $ CJ = 4x + 9$ and $ JT = 9x + 4$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {4x + 9} = {9x + 4}$ Solve for $x$ $ -5x = -5$ $ x = 1$ Substitute $1$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 4({1}) + 9$ $ JT = 9({1}) + 4$ $ CJ = 4 + 9$ $ JT = 9 + 4$ $ CJ = 13$ $ JT = 13$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {13} + {13}$ $ CT = 26$